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Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In…
We propose a logical framework combining a game-theoretic study of abilities of agents to achieve quantitative objectives in multi-player games by optimizing payoffs or preferences on outcomes with a logical analysis of the abilities of…
In a competitive sport, every little thing matters. Yet, many sports leave some large levers out of the reach of the teams, and in the hands of fate. In cricket, world's second most popular sport by some measures, one such lever---the…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
Fantasy football leagues involve strategic player trades to optimize team performance. However, identifying optimal trades is complex due to varying player projections, positional needs, and league-specific scoring. Existing approaches…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
The global rise of football analytics has rapidly transformed how clubs make strategic decisions. However, in India, the adoption of analytics remains constrained by institutional resistance, infrastructural limitations, and cultural…
We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among…
Composing a team of professional players is among the most crucial decisions in association football. Nevertheless, transfer market decisions are often based on myopic objectives and are questionable from a financial point of view. This…
Teams frequently compete on multiple fronts: political parties contest districts for majority control, contractors field specialized units to win procurement contracts, and squads play match by match for titles. Although the prize accrues…
The world of competitive Esports and video gaming has seen and continues to experience steady growth in popularity and complexity. Correspondingly, more research on the topic is being published, ranging from social network analyses to the…
From sports to science, the recent availability of large-scale data has allowed to gain insights on the drivers of human innovation and success in a variety of domains. Here we quantify human performance in the popular game of chess by…
In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game. This score quantifies the ex-post strategic ability of the…
We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…
In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies…
The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…
The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in…